Numerical methods for convection-diffusion problems or The 30 years war

Abstract

Convection-diffusion problems arise in the modelling of many physical processes. Their typical solutions exhibit boundary and/or interior layers. Despite the linear nature of the differential operator, these problems pose still-unanswered questions to the numerical analyst. This talk will give a selective overview of numerical methods for the solution of convection-diffusion problems, while placing them in a historical context. It examines the principles that underpin the competing numerical techniques in this area and presents some recent developments.